Amounts spent by a sample of 200 customers at a retail store are summarized in the following relative frequency distribution. The median amount will fall in the following class interval ____________.
A) 0 up to 10
B) 10 up to 20
C) 20 up to 30
D) 30 up to 40

Question

Amounts spent by a sample of 200 customers at a retail store are summarized in the following relative frequency distribution.  The median amount will fall in the following class interval ____________.
A) 0 up to 10 
B) 10 up to 20 
C) 20 up to 30 
D) 30 up to 40

Quizplus · Accepted Answer

To find the median, we need to first calculate the cumulative relative frequency, which is the sum of each frequency and all the frequencies below it.

Class Interval | Frequency | Relative Frequency | Cumulative Frequency | Cumulative Relative Frequency
--- | --- | --- | --- | ---
0 up to 10 | 36 | 0.18 | 36 | 0.18
10 up to 20 | 72 | 0.36 | 108 | 0.54
20 up to 30 | 56 | 0.28 | 164 | 0.82
30 up to 40 | 28 | 0.14 | 192 | 0.96
40 up to 50 | 8 | 0.04 | 200 | 1.00

The median is the middle value in the data set, which in this case is the 100th value (since there are 200 customers). Looking at the cumulative relative frequencies, we can see that the median amount falls in the third class interval, 20 up to 30, since the cumulative frequency at the end of that interval (164) is closest to (but not greater than) the middle value of 100. Therefore, the answer is choice C.

Amounts Spent by a Sample of 200 Customers at a Retail